3:30 pm Friday, November 20, 2015
Math Finance: The Pricing of Contingent Claims and Optimal Positions in Asymptotically Complete Markets by
Scott Robertson (Carnegie Mellon University) in RLM 9.166
In this talk, we will consider utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. To obtain this result, we draw motivation from and make connections to the celebrated Gartner-Ellis theorem from Large Deviations theory. Numerous examples will be given where the afore-mentioned price convergence takes place, including fixed markets with vanishing risk aversion, the basis risk model with high correlation and the Black-Scholes-Merton model with vanishing transaction costs. We will also show that the large claim regime could naturally arise in partial equilibrium models. Time permitting, we will discuss the main pricing assumption for general semi-martingale models and how it leads to a measure of market incompleteness, and how the optimal trading strategies are obtained. Submitted by
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